Difference between metaphor and simile

A metaphor is a figure of speech that directly compares two unlike things without using "like" or "as." It states that one thing is another.
A simile is a figure of speech that compares two unlike things using the words "like" or "as."

For example:
Metaphor: "The world is a stage." (The world is directly compared to a stage.)
Simile: "He is as brave as a lion." (Bravery is compared to a lion's bravery using "as.")